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| Mirrors > Home > MPE Home > Th. List > chvarvv | Structured version Visualization version GIF version | ||
| Description: Implicit substitution of 𝑦 for 𝑥 into a theorem. Version of chvarv 2401 with a disjoint variable condition, which does not require ax-13 2377. (Contributed by NM, 20-Apr-1994.) (Revised by BJ, 31-May-2019.) |
| Ref | Expression |
|---|---|
| chvarvv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
| chvarvv.2 | ⊢ 𝜑 |
| Ref | Expression |
|---|---|
| chvarvv | ⊢ 𝜓 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | chvarvv.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
| 2 | 1 | spvv 1996 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) |
| 3 | chvarvv.2 | . 2 ⊢ 𝜑 | |
| 4 | 2, 3 | mpg 1797 | 1 ⊢ 𝜓 |
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